The withdrawal of Electra Partners Europe follows strong rumours last month that MidOcean Partners, the other private equity firm shortlisted, had also lost interest in making an offer for the company after conducting an analysis of its future prospects.

LA Fitness, which was founded in 1990 by Fred Turok, its South African-born chief executive, who retains a 15.7 per cent stake, announced in December that it had appointed Close Corporate Finance to seek expressions of interest from potential buyers.

The decision marked something of a U-turn by Mr Turok who had steadfastly maintained that he did not want to follow rivals such as Esporta, Cannons and Fitness First in taking LA private with backing from a private equity firm.

Despite a sharp rise in the share price in the wake of that strategy, Mr Turok is understood to have become frustrated at the lack of support among institutional investors for his plans to consolidate the market through acquisitions.

In February, the group announced that trading during the crucial month of January had been only “broadly consistent” with its targets amid what it termed “a climate of aggressive competition”.

Although it insisted that it was still confident of achieving a good performance for the year to the end of July, the bidders are understood to have become concerned that the performance gap over its rivals had been narrowed.

Shares closed unchanged at 233½p, valuing the firm at about £96 million.

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